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Dynamics, Geometry and Groups Seminar

Speaker: Lingfeng Lu (Queen's University)

Title: Periodic orbits and transitivity of Anosov flows on (non-compact) 3-manifolds

Abstract:
A dynamical system is said to be transitive if it has an orbit that is dense in the ambient space. For hyperbolic dynamical systems, and in particular for Anosov flows, transitivity is closely connected to their periodic orbits. In this talk, we will first recall some classical results on this relationship for Anosov flows on compact 3-manifolds. Then together with the help of some more recent approaches, we will discuss a construction of transitive Anosov flows on non-compact regular covers of the ambient manifolds. If time permits, we will also discuss a criterion for transitivity on any regular abelian cover. This is joint work with Thomas Barthelmé.

Calabi-Yau Manifolds Seminar

Speaker: Rikuto Ito (Nagoya University)

Title: Genus Theory for Principal Rank-21 Cubic Fourfolds

Abstract: Lattice theory plays a powerful role in algebraic geometry. For example, oriented positive-definite even lattices of rank 2 correspond bijectively, up to isomorphism, to singular K3 surfaces (i.e., K3 surfaces with maximal Picard number), as established by the Shioda–Inose correspondence. While isomorphism of lattices is a global notion, lattices that are locally isomorphic need not be globally so; the set of such locally isomorphic lattices constitutes a genus. Describing a genus explicitly is useful for studying the degrees of fields of definition of algebraic varieties. In fact, for singular K3 surfaces, the degree of the field of definition can be bounded below by the number of elements in a certain genus (see Shimada 2006; Schütt 2007).

In this talk, I will present an explicit computation of the genus for principal rank-21 cubic fourfolds and explain how this yields a lower bound for the degree of their fields of definition.

Curves Seminar

Speaker: Calvin Fletcher

Affiliation: Queen's University

Title: Applications of the R-S-K correspondence and a first look at the Littlewood-Richardson rule

Abstract: Now that we have seen the R-S-K correspondence, in this talk we will explore some applications of it. Notably, we will establish a claim made in the very first talk, namely, that the Schur polynomials are symmetric. We will also get our first taste of the hook formula and see some interesting combinatorial applications. Finally, we will see the Littlewood-Richardson rule strictly in its tableaux counting form.

Algebra & Geometry Seminar

Speaker: Alexandra Seceleanu (University of Nebraska-Lincoln)

Title: Weighted Veronese rings

Abstract: 
The d-th Veronese subring of a graded ring R contains the homogeneous polynomials whose degree is a multiple of d. If R is a standard graded polynomial ring, its Veronese rings have excellent features such as being determinantally presented, having quadratic Gröbner basis, and satisfying the Cohen-Macaulay and Koszul properties. In this talk we investigate to what extent analogous properties hold for R a non-standard graded polynomial ring. This is joint work with Sankhaneel Bisui, Bek Chase, Luca Fiorindo, Thiago de Holleben, Emanuela Marangone, Thai Nguyen, and Srishti Singh.

Department Colloquium

Speaker: James G. Arthur (University of Toronto)

Title: 2025 Lorne Campbell Lecture: Modern discoveries in the unification of Mathematics

Abstract:
Mathematics today is going through an extraordinary period of unification. We are finding fundamental relations among vast areas of the subject —algebra, geometry, analysis, number theory— that have been studied for centuries. What does this mean? We shall discuss possible philosophical implications of the question. We shall then say something of the areas, and the relations among them, with an eye perhaps to recognizing some beauty in the way they all fit together.

Event Description:
The Lorne Campbell Lecture Series honours the work of Lorne Campbell, a professor in the Department of Mathematics and Statistics from 1963 to 1996 and Head of Department from 1980 to 1990. Professor Campbell, currently Emeritus at ���ϳԹ���Դ, was a Canadian pioneer in the field of communication theory. The lecture series is made possible through the generous donation of Dr. Vijay Bhargava, a former student of ���ϳԹ���Դ.

Department Colloquium

Speaker: Tushar Das (University of Wisconsin-La Crosse)

Title: From the division algorithm to fractals via dynamics: mathematics as centuries-long conversation

Abstract:
Iterating the ancient division algorithm gives birth to continued fractions, which have provided a natural playground for major developments in geometry, number theory, analysis, topology, stochastics, and dynamics. We will survey a small confluence of results (see https://arxiv.org/a/das_t_4.html) that flow across the fertile interfaces of geometric measure theory, dynamical systems, and Diophantine approximation. The colloquium will be accessible to students and faculty whose interests intersect the convex hull of the aforementioned subjects, the only prerequisite being curiosity. Perhaps most importantly, I will present a sampling of open questions and research directions that await exploration by the mathematical community at Queen's and friends beyond :)

Algebra & Geometry Seminar

Speaker: Adrian Zahariuc (University of Windsor)

Title: Interpolation of fat points on K3 and abelian surfaces

Abstract: This talk will be concerned with questions in the style of the Segre-Harbourne-Gimigliano-Hirschowitz (SHGH) Conjecture. I will sketch a proof of the fact that any number of general fat points of any multiplicities impose the expected number of conditions on the primitive linear system of a very general K3 or abelian surfaces of any degree/polarization. The proof relies on the Segal-Wilson formula for the vanishing of the theta function in the KP direction, and thus has a significant (although implicit) transcendental ingredient.

Curves Seminar

Speaker: Julia McClellan

Affiliation: Queen's University

Title: The Robinson-Schensted-Knuth Correspondence

Abstract: Equipped with the necessary tools developed in our previous discussions, we will explore how the row bumping algorithm gives a one-to-one correspondence between matrices of nonnegative integers and pairs of tableaux of the same shape. This is known as the Robinson-Schensted-Knuth correspondence. Through example, we will demonstrate a more “geometric” construction for this correspondence which does not rely on the bumping algorithm, called the matrix-ball construction.